The Joint Transform Correlator (JTC) correlates two inputs by taking the fourier transform of their joint fourier power spectrum. See FIG. 1 of U.S. Pat. No. 5,040, 140 issued to Horner et al. A reference, r(x,y), and a scene, s(x,y), are displayed side by side in the input plane. The input images are offset from the optical axis by distances x.sub.1 and x.sub.2, yielding an input: EQU input(x,y)=r(x-x.sub.1, y)+s(x-x.sub.2, y) (1)
A lens is used to form the fourier transform of the input plane on a detector. The result is the joint fourier power spectrum of the inputs: EQU .vertline.T(.alpha.,.beta.).vertline..sup.2 =.vertline.R(.alpha.,.beta.).vertline..sup.2 +.vertline.S(.alpha.,.beta.).vertline..sup.2 +2Re{R* (.alpha.,.beta.)S(.alpha.,.beta.) exp j2.pi..alpha.(x.sub.1 -x.sub.2)!}(2 )
The output from the first stage of the JTC is used as the input to a second fourier transform stage. The result of this transform is the correlation of the input plane with itself. ##EQU1## Here the .star-solid. symbol denotes correlation.
Both auto-correlation and cross-correlation products are present in the JTC output. The reference and the scene will both auto-correlate to a peak centered at the coordinates (0,0). The center of the cross-correlation outputs will be displaced from the optical axis by the distance .+-.(x.sub.1 +x.sub.2).
A source of difficulty is that the reference and scene auto-correlation signals often dominate the output. If the self-correlation spectra are broad, these signals can overlap the cross-correlation outputs. This is particularly troublesome in the multiple target scenario. If a feature in the input scene is repeated, the cross-correlations between instances of the repeated feature appear as correlation peaks in the output plane.
The traditional solution is spatial separation of the inputs. If the reference and scene are far apart in the input plane, there will be regions of the output plane which correspond only to valid cross-correlations. This is because the distance involved between the two correlating objects will require that one be located in the scene and the other be in the reference. Correlations detected at shorter distances are assumed to be self correlations and are ignored. This solution works well, but it is not ideal since much of the input scene must be filled with blank space to provide the necessary separations. Also, the auto-correlations remain a major noise source, even when their peaks are not in the valid cross-correlation area.